Simplify the following expression: $ r = \dfrac{-1}{7} + \dfrac{10n + 4}{-9} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-9}{-9}$ $ \dfrac{-1}{7} \times \dfrac{-9}{-9} = \dfrac{9}{-63} $ Multiply the second expression by $\dfrac{7}{7}$ $ \dfrac{10n + 4}{-9} \times \dfrac{7}{7} = \dfrac{70n + 28}{-63} $ Therefore $ r = \dfrac{9}{-63} + \dfrac{70n + 28}{-63} $ Now the expressions have the same denominator we can simply add the numerators: $r = \dfrac{9 + 70n + 28}{-63} $ $r = \dfrac{70n + 37}{-63}$ Simplify the expression by dividing the numerator and denominator by -1: $r = \dfrac{-70n - 37}{63}$